Our approach is similar in spirit to the drift method (see Section ). However, our construction of the Lyapunov function cannot be derived using existing methods as in [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]} and instead requires new insights. In particular, we find a Lyapunov function whose drift has an interesting upper-bounding function, which then allows us to establish an upper bound on the queueing probability.
Our Lyapunov function also has an intuitive meaning: it corresponds to the total work contributed by all the jobs in the system.
Here the work contributed by a job is the product of its server need and its expected service time. More details on the drift method and the steps in our approach are given in Sections REF  and REF .
